Variation of solution with time steps in transient linear convection solution

Matlab code and plots :

https://drive.google.com/open?id=1qGelFTYqH1oflTifB_wm1bJj1R5eMRs1

The variation in the velocity profile can be seen in the above plot. As the value of time step increases, the profile starts diffusing or loosing energy. The velocity starts decaying and the second order diffusion effects can be seen in the time step of 0.1 . This is where the diffusion effects can be seen distinctively.

While solving the transient linear convection, we assume that the secord order differential terms to be negligible. This exclusion yields the appearance of diffusion when the time step gets larger.